Line Simplification with Restricted Orientations
نویسنده
چکیده
We study the C-oriented line simplification problem: Given a polygonal chain P represented by an ordered set of vertices PI , ... , pn in the plane, a set of orientations C, and a constant c, we search for a "C-oriented" polygonal chain Q consisting of the minimum number of line segments that has distance at most c to P in the Frechet metric. A polygonal chain is C-oriented if the line segments are parallel to orientations in C. We restrict our attention to the version of the problem where two circles of radius c formed around adjacent vertices of the polygonal chain do not intersect. We solve the C-oriented line simplification problem constructively by using dynamic programming together with a nice data structure. For usual cases of C our algorithm solves the problem in time O(kn2 Iog(n)) where k is the minimum number ofline segments of Q and uses O( kn 2 ) space.
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